Spin-based electronics is an emerging disruptive technology with enormous potential. A promising application is the field of computer memories, where Magnetoresistive Random Access Memories (MRAM) could replace the present memory technologies.
The rapid progress in the miniaturization of semiconductor electronic devices leads to a degree of integration where quantum effects will take precedence over classical electronic effects. Electron spin being one such quantum effect, Spintronics—short for spin-based electronics—involves devices where both the charge and spin of an electron are used to carry and manipulate information. Applications for spintronics-based devices include Giant Magnetoresistance (GMR), Magnetic Sensors, Magnetoresistive Random Access Memories (MRAM), Spin Transistors and Quantum Computing for example.
GMR represents a quantum technology that was successfully commercialized, with applications in the data storage industry, principally for hard disk drives. Today almost all hard disk drives are based on this technology.
MRAM has the potential to revolutionize and take over the memory market. MRAM technology is based on the use of magnetic moments, rather than on electric charge, to determine the on-off state of the memory bit cell. MRAM combines the best attributes of three major existing memory technologies: density of DRAM (dynamic RAM), the speed of SRAM (static RAM) and the nonvolatility of flash memory.
Magnetic sensors have the potential to be directly fabricated on silicon substrate, leading to highly efficient systems where sensing and logic functions are closely integrated. In spin-based quantum computers that have been conceptually envisioned, the fundamental unit to represent information is quaternary (rather than binary), which opens the door to new computing techniques especially well adapted to deal with non-linear problems and suitable for massively parallel computing applications. Magnetic sensors known as Anisotropic MagnetoResistance (AMR) sensors can be presently manufactured at a reasonable cost, providing arrays of sensors built-in on a silicon substrate. These find applications in magnetic biosensing, non-destructive testing, position sensing, document validation and magnetic imaging. Due to a number of technical shortcomings caused by the AMR effect exploited in these sensors, magnetic tunnel junction (MJT) sensors may progressively replace AMR sensors. Since MRAMs are MJT devices, the development of MJT sensors will be closely tied to the advances made for MRAMs.
As for spin-based transistors and quantum computing, these technologies are still at their infancy, and further research and development are needed before commercial applications become available. Spin-based transistors offer an alternative for smaller energy consumption and faster performance.
It is expected that GMR will continue to be a driving market force for spintronics until MRAM takes off and becomes widely commercially available. In the short term, the hard-disk market is expected to continue to be a primary driver for technological advancement, pulled by a constant need to increase the data storage capacity that leads to devices with increased surface density. With already some initial success for applications in the space and military domains, MRAM is just entering the commercial market. Prototypes of MRAM-based products are presently available and it is expected that commercially viable products will be soon available. Continuous research and development activities in the fields of magnetic device elements, magnetic materials and process integration for magnetic components will allow the technology to further develop and to eventually become widely commercially available. In the long term, MRAM may become a memory for many applications, since it is at the same time nonvolatile, durable, fast and dense, and thus eliminates the need to combine memories of different types. It has the potential to be used for a wide range of applications such as mobile phones, digital cameras, game consoles, personal digital assistants/organizers, personal computers, automobiles, etc.
The broad adoption of spintronics depends on a number of restraining factors that still constitute considerable challenges, at least in the short term. One first such factor relates to the production of semiconductor devices with new materials. Indeed, spintronics do not use the same materials used in conventional semiconductors. Since spintronics devices use magnetism, metallic substrates are usually needed. Materials that find applications in spintronics include nickel, iron, cobalt and their alloys and other compounds. Their use in conjunction with traditional semiconductor materials results in challenges in terms of compatibility, integration, etching, patterning, and production. A second challenging factor is the reliability of spintronics device, which is not demonstrated yet. A third restraining factor might be the fact that MRAMs requires high current for the magnet to switch between states, which causes problem for low-power operation.
Methods that can accurately model performance of modern hard-drives and magnetic memory (MRAM) and aid in the design process and evaluation of future technology have thus become essential. As the devices continue to downsize into the nanoscale limit, currently available modeling methods are no longer adequate or even valid, and new methods are needed to continue to support research and development.
The tunnel magnetoresistance (TMR) effect in systems with spin-polarized transport is emerging as a basic physical principle for near-future information storage technology, magnetic sensor, magnetic random access memory (MRAM), magnetic programmable logic, as well as spintronics (see W. J. Gallagher et al. IBM Res. & Dev., Vol 50. 5-23A (2006)).
TMR devices typically comprise an insulating (I) tunnel barrier separating two ferromagnetic (FM) metal layers in the form of FM-I-FM, as shown in FIG. 1 for example (W. Butler, Nature Materials, 3, 845 (2004)). Crucial to the development of TMR technology is the material and device design automation. At present, since the insulating layer (I) is only a few atomic layers thick, even a few impurities and/or defects may have substantial quantitative influence to device operation. Furthermore, since TMR is a quantum mechanical effect, a proper design automation method should be based on atomistic quantum mechanical first principles. Such a method should be able to predict how spin-polarized charge transport is related to atomic structure, and how TMR depends on external control parameters such as voltage and temperature.
TMR effect will be briefly described in relation to FIG. 1. It is found experimentally that when the magnetic moments of two ferromagnetic layers 1 and 2 are antiparallel (AP), the tunnel resistance RAP across the tunnel barrier is large, i.e. the tunneling current IAP is small; whereas, when the moments are parallel (P), the tunnel resistance RP is small, i.e. the tunneling current IP is large. The switching between large and small resistances is therefore achieved by the relative orientation of the magnetic moments in the two FM layers.
For MRAM application, RAP and RP are used as “1” and “0” in a non-volatile memory device. In information storage or magnetic sensor application, an external magnetic field (from the magnetic bits in a media, for example) flips one of the moments, leading to a change of tunneling current, which is then detected.
An important device parameter is the magneto-resistance ratio, defined by RAP and RP as: R=(RAP−RP)/RP=(IP−IAP)/IAP: the greater R, the more sensitive the device becomes, which is desirable. While magnetic tunnel junctions have been studied for many years, it was only very recently that large values of R have been achieved at room temperature, leading to commercial applications of TMR.
FIG. 2 illustrates enhancements of TMR ratio at room temperature, due to the discovery of the MgO tunnel barrier (M. Coey, Nature Materials, 4, 9 (2005)). In addition to oxide barriers, there has been other research on devices where the barrier is a single molecular layer or even a single molecule. These molecular TMR devices include carbon nanotubes (K. Tsukagoshi, B. W. Alphenaar and H. Ago, Nature, 401, 572 (1999).), organic semiconductors (Z. H. Xiong, Di Wu, Z. Valu Vardeny and Jing Shi, Nature, 427, 821 (2004)), and organic molecules (J. R. Petta, S. K. Slater and D. C. Ralph, Phys. Rev. Lett. 93, 136601 (2004)), sandwiched between Ni, Co and Fe materials. The TMR ratio in these molecular devices is typically around 10-20% at present, pointing to substantial room for further improvements.
The rapid progress in TMR technology, as exemplified in FIG. 2, is in part due to better material preparation and control. It is also directly related to an increased understanding of the basic physics of spin polarized quantum transport. Indeed, the theoretical prediction (W. H. Butler et al. Phys. Rev. B 63, 054416 (2001)) of coherent tunneling coupled to symmetry of electron wave function in Fe—MgO interface contributed to the experimental discovery of the large TMR.
In order to rapidly develop TMR technology to large-scale commercialization, an atomistic modeling method of quantum transport is needed for assisting experimental work. This is especially true due to the fact that there still exist many experimental facts that have not been understood. For instance, while theoretical prediction (W. H. Butler et al., Phys. Rev. B 63, 054416 (2001)) of TMR ratio for Fe—MgO—Fe device can be greater than several thousands, experimental results (as exemplified in FIG. 2) are still considerably lower. The reason may be related to the quality of the atomic arrangement at the Fe/MgO interface, the existence or absence of oxygen vacancies and/or other defects. More importantly, much experimental data (S. S. P. Parkin et al. Nature Materials, 3, 862 (2004); S. Yuasa et al., Nature Materials, 3, 869 (2004)) show that the TMR ratio is monotonically decreased by applied bias voltage and reduces to zero when the voltage is about 0.5-1.0 volt. Published theoretical work to date predicted a substantial increase of TMR by bias for systems with asymmetric atomic structure (C. Zhang et al., Phys. Rev. B 69, 134406 (2004)). It is clear that all the modeling methods presented in literature, while useful for academic research, are not capable of making quantitative predictions of spin-polarized quantum transport for practical TMR devices at the atomistic level under nonequilibrium conditions.
Theoretical modeling of spin-polarized transport including atomic and material properties is a very difficult problem.
In DFT, as described in the art, the Hamiltonian operator Ĥ of a system is determined as a functional of a local electron charge density ρ(r), i.e. Ĥ=Ĥ[ρ(r)].
In a transport problem, the system has open boundaries connecting to electrodes and operates under external bias and gate potentials, which drive the device to non-equilibrium: in other words, the environmental-group of the system comprises one or more electrodes and possibly metallic gates and substrates where the device is embedded, and the device-group is the electronic device scattering region, which comprises at least one atom. The charge density ρ(r) is thus to be determined under such conditions. Obtaining Ĥ and ρ(r) is a self-consistent process, wherein Ĥ is obtained from ρ(r), and then, using Ĥ, ρ(r) is evaluated, in an iterative process until Ĥ converges. The nonequilibrium device conditions may be accounted for by using the Keldysh non-equilibrium Green's function (NEGF) for example, to construct ρ(r) from Ĥ.
Indeed, as known in the art, the NEGF-DFT formalism is able to calculate charge density ρ(r) for open quantum device systems under a bias voltage entirely self-consistently without depending on using phenomenological parameter. Since the charge density ρ is constructed from NEGF, the non-equilibrium nature of the device can be handled properly. Atoms in the device scattering region and in the electrodes are treated at equal footing, therefore allowing a realistic electrodes and contacts modeling. NEGF treats the discrete and the continuum parts of the electron spectra at equal footing, so that all electronic states are included properly into the calculation of the device Hamiltonian H.
It is to be noted that NEGF-DFT has already been applied to devices with sizes and complexities no other self-consistent atomistic formalism of the art could handle. However, it still cannot be used for spin polarized charge transport in 3-dimensional magnetic devices.
The existing atomistic modeling methods for TMR devices can be roughly categorized into three classes:                (i) Non-self-consistent tight binding methods can account for some qualitative features of transport, but they depend on semi-empirical parameters thereby having limited predictability (H. Mehrez et. al. Phys. Rev. Lett. 84, 2682 (2000); S. Krompiewski, R. Gutierrez, and G. Cuniberti, Phys. Rev. B 69, 155423 (2004); E. G. Emberly and G. Kirczenow, Chem. Phys. 281, 311 (2002).).        (ii) Layer-KKR method with DFT is a self-consistent method for electronic structure (W. H. Butler et al., Phys. Rev. B 63, 054416 (2001); C. Zhang et al., Phys. Rev. B 69, 134406 (2004); J. M. MacLaren et. al., Phys. Rev. B 59, 5470 (1999)). After DFT is numerically converged, transport properties are computed by applying atomic sphere approximation (ASA). ASA is, in fact, an “art” and the results often depend how it is applied (For example, it has been shown that calculated tunneling conductance of Fe—GaAs interface sensitively depends on how ASA is applied, making quantitative predictions very difficult to make. K. Xia, private communication (2005)). This method has difficulty when there is an external bias voltage, for instance it predicted an increase of TMR ratio rather than the experimentally observed decrease as the bias is increased (C. Zhang et al., Phys. Rev. B 69, 134406 (2004)). Finally, the method requires very large computational time; and it is unclear if a bias and gate voltage can be modeled. This method is limited for application in systems consisting of layers of materials.        (iii) LMTO method has also been successfully applied to investigate TMR systems at zero bias voltage (K. M. Schep, et al., Phys. Rev. B 56, 10805 (1997); K. Xia, et al. Phys. Rev. B 63, 064407 (2001)). It is also based on ASA, and has difficulty in applying to non-space filling situations such as molecular TMR structures. In addition, at present no LMTO methods for TMR device simulation has and can include a bias voltage in the required self-consistent manner. Present implementations of this method can only be applied to bulk materials or layered bulk materials without external bias or gate voltage.        
The above existing methods prove to be limited in their application domain. In particular, they have only been applied to bulk systems at zero external potential.
Therefore, there is a need for a state-of-the-art atomistic quantum transport modeling method and associated method that is capable of filling the gap of TMR modeling for industrial applications.
The present description refers to a number of documents, the content of which is herein incorporated by reference in their entirety.